Time and Work

Time and Work

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Question 1
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
A
1/4
B
1/10
C
7/15
D
8/15
Question 1 Explanation: 
A's 1 day's work =115 B's 1 day's work =1/20 (A + B)'s 1 day's work =(1/15+1/20)=7/60 (A + B)'s 4 day's work =(7/(60*4))=5/15 Therefore, Remaining work =(1 - 7/15)8/15
Question 2
A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
A
46/5 Days
B
47/5 Days
C
48/5 Days
D
49/5 Days
Question 2 Explanation: 
(A + B + C)'s 1 day's work =1/4 ; A's 1 day's work =1/16; B's 1 day's work =1/12; Therefore C's 1 day's work =(total-A-B)=1/4-1/16-1/12 =5/48 So, C alone can do the work in 48/5
Question 3
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A
12 days
B
15 days
C
16 days
D
18 days
Question 3 Explanation: 
A's 2 day's work =(1/20)*2=1/10; (A + B + C)'s 1 day's work = 1/20+1/30+1/60=1/10 Work done in 3 days =1/10+1/10=1/5 Now, 1/5 work is done in 3 days.5 Whole work will be done in (3 x 5) = 15 days.
Question 4
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in: ?
A
20 days
B
45/2 days
C
25 days
D
30 days
Question 4 Explanation: 
Ratio of times taken by A and B = 1 : 3. The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day. If difference of time is 2 days, B takes 3 days. If difference of time is 60 days, B takes (3/2)x60= 90 days. So, A takes 30 days to do the work. A's 1 day's work =1/30 B's 1 day's work =1/90 (A + B)'s 1 day's work =1/30+1/90=4/90=2/45 A and B together can do the work in 45/2
Question 5
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A
Rs. 375
B
Rs. 400
C
Rs. 600
D
Rs. 800
Question 5 Explanation: 
C's 1 day's work =(1/2-1/6-1/8=1/24 A's wages : B's wages : C's wages =1/6:1/8:1/24 = 4:3:1 C's share (for 3 days) = Rs.(3*(1/24)*3200)=400
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